[Captain Tom Coughlin]

That's not really an answer. I asked a very specific question, I didn't ask why people may choose to settle new worlds. I asked why people living within the Federation would accept jobs that nobody would want to do. Why go to that job when you can literally do anything else you want?

You can't use examples of things people may want to do as an answer to the question of what would motivate people do the work that nobody wants to do.

Why scrub a power conduit when I can play catch with the kids or swim in the ocean?

[horatio]

As I already said I do not view the UFP as a moneyless society. You need pecuniary incentives to indirectly force people to do the less popular work.
The UFP is neither some stupid communist utopia nor is it a capitalist society. It is something in between. Independent of Trek I view this as the best possible society. Like so often the truth is somewhere in the middle. Of course this is not merely my irrelevant opinion, by any economic indicator Scandinavia kicks a*s.